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 |    Not for the faint of art. |
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Complex Numbers A complex number is expressed in the standard form a + bi, where a and b are real numbers and i is defined by i^2 = -1 (that is, i is the square root of -1). For example, 3 + 2i is a complex number. The bi term is often referred to as an imaginary number (though this may be misleading, as it is no more "imaginary" than the symbolic abstractions we know as the "real" numbers). Thus, every complex number has a real part, a, and an imaginary part, bi. Complex numbers are often represented on a graph known as the "complex plane," where the horizontal axis represents the infinity of real numbers, and the vertical axis represents the infinity of imaginary numbers. Thus, each complex number has a unique representation on the complex plane: some closer to real; others, more imaginary. If a = b, the number is equal parts real and imaginary. Very simple transformations applied to numbers in the complex plane can lead to fractal structures of enormous intricacy and astonishing beauty. ![Merit Badge in Quill Award
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| As an Aquarius, I don't believe in astrology. http://nautil.us/issue/81/maps/why-astrology-matters Why Astrology Matters Seeing meaning in the stars is a vital part of the scientific story. What I do believe in is folklore. Allow me to elucidate. Whether a thing reflects actual reality or not matters when one is discussing science, but not in every situation. For example, our concept of the beginning of the universe popularly known as the Big Bang fits all available data, and has made accurate predictions, while the Hopi creation story  (to name but one of many) serves as a window into the thought processes of that culture but no one is going to do effective science with it.These stories are culturally significant not only to their parent cultures, but to our understanding of humanity as a whole. And that is why, even though astrology is clearly bullshit, it's important to know about as part of the history of the stories we humans tell ourselves to try to make sense out of a nonsensical universe. And that, I think, is the theme this article's author is trying to convey. The basic premise of astrology is the stars and the planets exert an influence over events on Earth. It's actually a bit more complicated than that. Of course stars and planets exert an influence. The gravity of the sun and moon is obvious. The light of all the heavenly bodies reaches our eyes, and we can see them, however faintly and sometimes only through instruments. The idea behind astrology is that their relative positions matter, and that's the part that's, at best, mythological in nature. To the informed scientific mind—a relatively new phenomenon—astrology can’t possibly work. Like I said. Some might walk away at this point, seeing no value in discussing astrology. However, astrology is a vital part of our human, and scientific, story. We have been making astrological connections—mapping the heavens and trying to discern their influence on the Earth—for much longer than we have been doing science. Which is what I've been saying. Astrology had a huge influence on the development of science, sometimes directly. In 1663, Isaac Newton bought a book on astrology at the Sturbridge Summer Fair. It was an act of curiosity, but Newton found that he couldn’t make sense of it because he didn’t know enough geometry. And so he began to study Euclid. This is how Newton got hooked on mathematics. That's actually something with more grounding in fact than the possibly-apocryphal "falling apple" story. Like ancient AI, it was the job of astrologers to identify patterns in the gathered data and extract meaning from the correlations they found. Who can blame them if they sometimes saw patterns and meaning where there were none? That's what we humans do: look for patterns. As I've noted before, we often find them when they're not really there. But sometimes, in the searching, we stumble across deeper truths. In the end, Boxer, like me, doesn’t think there is any reason to believe in astrology—but we are both Tauruses, so what can you expect? Filthy Tauruses, stubbornly never getting anything right... oh wait, they're right. I’m not ashamed to say that I have a soft spot for astrology. Historically, astrology is the grit that seeded the pearl; its data-gathering, map-making, and pattern-seeking laid the cognitive foundations for modern science. Rather than rudely dismiss it as an embarrassing product of ignorant times, we should acknowledge its contribution. And that's the sense in which I discuss it -- as a relic, a step on the road to enlightenment, but certainly not enlightenment itself. This is how science works. You make observations. You gather data. You form hypotheses. You test the data from the observations to see if they conform to a hypothesis. If they don't, ideally, you throw out the faulty hypothesis. In the case of astrology, and in several other cases from human history that I won't go into right now, instead of throwing out the hypothesis, we've said, "Well, maybe if we just tweak the hypothesis..." Astrology claims to predict. And, just as a blind dart-thrower will occasionally hit a target through sheer chance, sometimes its predictions seem accurate. We'll always remember these accurate predictions -- the author of the linked article opens with one such. We'll either dismiss all the times the dart-thrower hit the backboard (or his friend standing too close to it), or we'll make excuses for him. "Well, that was just one bad throw." The article itself is interesting in that it describes, also, some attempts to get at the accuracy rate of astrology; so far, it seems indistinguishable from blind chance. As for the gravitational influence of the planets upon one's birth, keep in mind that -- and I haven't run the numbers here, so take this with a grain of salt -- the obstetrician exerts a greater gravitational field on the newborn than does the mighty planet Jupiter, all those millions of miles away. Nevertheless, we are influenced by Jupiter, and by Mars and Venus: we're influenced to want to go out there and explore, or stay here and send robot probes. The planets and the stars do have repercussions on our lives, if only indirectly. Just not in the way the astrologers claim. Theirs is the power of stories, of discovery, of speculation. And that's more powerful than gravity. An explanation of today's blog entry title |
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